Most of the methods proposed so far for numerical analyses of all-optically regenerated transmission systems have problems either in strictness or in simplicity, which are trade-off. In this paper, a new statistic approach is proposed, which is based on probability distribution functions (PDFs) of transmitted signals and a transfer function of an all-optical regenerator. The method is simple since complicated calculation of the device dynamics is not necessary, while it is strict as the conversion of PDF by the nonlinear transfer function is rigorously calculated.